I know! Too many facts. Playing with curves invites ideas. Putting them together differently leads to beautiful designs. Figuring out how to code them has caused deep thinking. Curve stitching inspires wonder and encourages questions to be asked and answered years before taking precalculus.
I began to think. What if I made a frame that looks like an old-fashioned television screen?
The four pieces (one per corner) would be half the size of those on the fancy frame. This step points to a key element of problem-solving: break the process down into smaller steps and conquer the problem one step at a time.
If not, make a quick sketch of the television screen and cut it out along the edge. Cut it into four equal pieces. Treat the pieces like manipulatives and make a cross by moving them.
Then, I realized something! When tutoring someone in precalculs, I looked up how to change a formula to shift the curve to another point. This tangible process helped me see that all you need to do is adding a positive or negative number to the original coordinates. Reflection requires the x and y coordinates to swap places. From now on, all I need to do is recall curve stitching!
How do you start? Here is a quick tour. First read my post, Curve Stitching Roundup, an orderly review of what curve stitching is, who invented it, and interesting variations. Since that post, I've added a few elaborations: six-petal flower, picture frame, valentine I, valentine II, and valentine III.